Rope sawing machines are already known with which the sawing rope is slung in the form of an endless loop around a concrete body or the like that must be cut. As the depth of the cut increases, to maintain the cutting pressure of the rope, the sawing rope loop must be continuously lightened. To this end the rope driving device is positioned on a carriage or traveller that can be moved along horizontal rails. When large bodies must be cut, long rope loops, a long travelling path and correspondingly long rails are required. In many cases, however, a limited availability of space prevents the installation of long rails, which limits the use of such rope sawing machines.